The correct answer is (C) OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
What is line?
A one-dimensional geometric figure that consists of infinitely many points arranged in a straight path or direction.
In this case, we are reflecting across the line y = -2, which is two units below the x-axis. Therefore, the y-coordinate of each point in the preimage will be changed by 2 units after reflection.
The coordinates of L are (-1, -6), and after reflecting across y = -2, the y-coordinate will become
-6 + 2 = -4
Therefore, the image of L, L', will have coordinates (-1, -4).
Looking at the given options:
A. L'(-3, 6) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
B. OL'(-1,6) - This point is above the reflected line y=-2, so it cannot be the reflection of L.
C. OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
D. OL(1, 2) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
Therefore, the correct answer is option C: L'(-1, -4).
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Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum of the given function for this region.
Using inequalities, Y(x=0) = -2 and X(y=0) = -2 in region 1.
To pick area 1, draw a line at the intersection of (-2,0) and (0, -2), then choose the right side. such as.
Region 2) To pick the region to the left or upwards in region 2, we must draw a line from (0,2) to (-2,4).
Y(x=0) = 2\sX(y=-2) = -4
Region 3) To pick the region to the right, we must draw a line connecting (-4,0) and (0,4), as I'll demonstrate.
What are inequalities?Inequalities in mathematics describe the relationship between two non-equal numbers. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, several inequalities are utilised to compare the numbers, whether it is less than or higher than.
The feasible area is now visible. Let's determine the vertices' coordinates.
Where the blue and green lines intersect is our first vertex.
3x + 2 = x + 4 and y = 3x + 2
3x - x = 4 - 2
y = 3× (1) + 2 = 3 + 2 = 5 when 2x = 2x = 1
(X, Y) = Vertex 1 (1,5)
The intersection of the red and green lines is at vertex #2:
y = -x -2; y = x + 4; y = x + 4 = -x - 2; and y = x + x = -2 - 4
2x = -6, x = -6/2, and y = (-3) + 4 = -3 + 4 = 1 are the results.
(X, Y) = Vertex 2 (-3,1)
The intersection of the red and blue lines is at vertex 3:
y = -x - 2, y = 3x + 2 -x - 2, and y = 2 + 2 -4 x = 4 x = -4 / 4 = -1.
So, y = 3× (-1) + 2 = -3 + 2 = -1
(X, Y) = Vertex 3 (-1, -1)
Let's now modify the graph by including the supplied equation.
The intercept where Y=0 is 0 is given by f(x,y) = -3x + 5y = 0 5y = 3x + 0 y = 3/5 × X + 0
the gradient m = 3/5
A line can be drawn from (0,0) to (-10, -6)
Let's now examine how it would appear in the area where it is practical.
We can see that the function intercepts the blue line or the line of the second section, which is where the largest value is located.
y = 3x + 2 3x + 2 (3/5 - 3) x = 2 -12/5 × x = 2 x = -5/6.
Hence, y = 3x + 2 3/5 × (-5/6) = -1/2.
The maximum is therefore found at (x,y) = (-5/6, -1/2).
The point where the function crosses the red line now marks the minimum.
y = 3/5 × x; y = -x -2
3/5 x = -x - 2\s (3/5 + 1) × x = -2\s8/5 x = - 2\sx = -2× (5/8) = -5/4.
y = 3/5 × (-5/4) = -3/4
The minimum is thus found at (x,y) = (-5/4, -3/4)
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graph the line with y-intercept 1 and slope 4
Answer:
y = 4x + 1
Step-by-step explanation:
Let's graph it in slope intercept form y = mx + b
m = the slope
b = y-intercept
m = 4
b = 1
So, the equation is y = 4x + 1
Kristoff needs to fill in the blanks below to factor x2 - 12x + 20. Which of the following is
NOT true about the missing values?
The factor that both trinomials have in common is; C: (x + 2)
How to factor polynomials?In mathematics, a polynomial is defined an expression that consists of variables that are also referred to as indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² - 7x - 18
The trinomial of james is;
x² - 7x - 18
Factorizing this gives;
x² + 2x - 9x - 18
= x(x + 2) - 9(x + 2)
= (x + 2)(x - 9)
The trinomial of Kaitlin is;
x² + 14x + 24
Factorizing this gives;
x² + 12x + 2x + 24
= x(x + 12) + 2(x + 12)
= (x + 2)(x + 12)
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what is Net profit?
Answer:
Net profit is the amount of money that a company has earned after deducting all of its expenses, taxes, and other costs from its total revenue. It is the final result of a company's income statement, which shows the revenue, expenses, gains, and losses incurred during a specific period of time, typically a year. Net profit is often used as a key measure of a company's financial performance and is a crucial metric for investors and stakeholders in evaluating the success of a business.
Step-by-step explanation:
Use the diagram of the cylinder to answer the question. Use 3.14 for π and round to the nearest tenth. SHOW PROOF PLEASE
803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.
What is the surface area of a solid?Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.
According to the given information:The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given values, we get:
Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8
= 401.92 + 401.92
= 803.84 square inches
the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.
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Integers of 7° F below 0
The integer number that represents a temperature of 7 ºF below zero is given as follows:
-7 ºF.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For temperatures, we have that:
Temperatures above 0ºF are positive.Temperatures below 0ºF are negative.Hence the integer number that represents a temperature of 7 ºF below zero is given as follows:
-7 ºF.
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Complete the equation of the line through (2,1) and (5,-8) in y=Mx+b form
Answer:
y=-3x+7
Step-by-step explanation:
find the slope which is (y1-y2)/(x2-x1). therefore the slope is -3. and then put it in point slope intercept form which is (y-y1)=m(x-x1) = (y-1)=-3(x-2) and simplified the expression is y=-3x+7.
PLS HELPPP THYANK UUU PLS The data below shows the colors preferred by a group of people. We want to plot this on a pie chart. What will be the central angles of each of these categories?
Red=
blue=
green=
purple=
Answer:
Red 100
Blue 150
Green 50
Purple 60
Step-by-step explanation:
The total number of people surveyed
= 20 + 30 + 10 + 12
= 72
The relative area of each pie in the pie chart will be in the ratio of
number of people who prefer a color ÷ total number of people
The central angles of each pie category = above ratio x 360°
Fraction of people who prefer red = 20/72These angles should add up to 360°
100 + 150 + 50 + 60 = 360
complete the table 8 to 16 __ to 1 __ to 10 __ to 17
The values in the table using the expression (time=2 × no. of pages) will be 0.5, 5 and 8.5.
What exactly are expressions?In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to produce a value.
Expressions can be simple or complex, and can involve arithmetic, algebraic, or logical operations. Some examples of expressions include:
5 + 3x - 2y(a + b) / (c - d)In each of these examples, the expression consists of one or more terms that are combined using operations such as addition, subtraction, multiplication, division, or exponentiation.
Now,
As given pages = 8 and time= 16 minutes
this can be deduced by expression Time=2 × no. of pages
Then for time= 1,10 and 17 minutes
no. of pages will be 1/2,10/2 and 17/2.
Hence, the table will be:
Pages 8 0.5 5 8.5
Minutes 16 1 10 17
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Y=4x^2;estimate dy/dx x=2
Answer:
Below
Step-by-step explanation:
y = 4x^2
dy/dx = 8x
at x = 2 this is 16 <===== not sure what they mean by 'estimate' !
Mr. and Mrs. Smith took their children on a trip to the Grand Canyon. When they left home, Mrs. Smith noted the odometer read 5,478.18 miles. When they arrived at the Grand Canyon, she noted that the odometer read 6,010.63. How far had the family-driven?
Mr Smith looks their children 1 times 1
Identify the equation for the graph shown.
A. y = 5x - 2
B. y = 2x - 5
C. y = 2x + 5
D. y = x - 4
E. y = 2x - 6
Latanya needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 739 glasses. There are currently 390 glasses. If each set on
sale contains 6 glasses, which inequality can be used to determine x, the minimum
number of sets of glasses Latanya should buy?
A. 739 6x + 390
B. 390x+6739
C.390x+6> 739
D. 739 2 6x +390
Submit Answer
The inequality that can be use to represent the situation is 390 + 6x ≥ 739.
How to represent expression with inequality?Latanya needs to order some new supplies for the restaurant where she works. The restaurant needs at least 739 glasses. There are currently 390 glasses. Each set on sale contains 6 glasses.
Therefore, the inequality that can be used to determine x, the minimum number of sets of glasses Latanya should buy can be calculated as follows:
Hence,
390 + 6x ≥ 739
where
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The function f is graphed below. Determine the intervals on which f is increasing and decreasing.
The function is decreasing on the interval -6 < x < 0
increasing on the interval 0 < x < 4, and increasing on 4 < x < 9
A cat adoption facility takes in an average of 6 cats per day. The facility has to keep their cat occupancy below 300. Currently, the facility has 258 cats. If none of their cats get adopted, how many more days, x, can the facility continue to take in cats? Select the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit.
A. x < 5
B. x < 7
C. x < 42
D. x < 36
The highest number of days this institution can continue to accept cats without going over its allowed occupancy is included in the inequality (C) x<42.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.
Hence, inequality emerges from a lack of balance.
So, what we can do is add 6 in 285 till it reaches 300.
258 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 300
6 is added 7 times, then:
6*7 = 42
Then the correct inequality would be x < 42.
Therefore, the highest number of days this institution can continue to accept cats without going over its allowed occupancy is included in the inequality (C) x<42.
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Problem is down below Please find the answer.
[tex](2x-1)^{2} = 25 \iff (2x-1)^{2} = 5^{2}\\[/tex]
[tex]x > 0 \implies 2x - 1 = 5 \iff 2x = 5 + 1 \iff 2x = 6 \implies \bf x = 3\\[/tex]
[tex](3y-1)^{2} = 36 \iff (3y-1)^{2} = 6^{2}\\[/tex]
[tex]y > 0 \implies 3y-1 = 6 \iff 3y = 6 + 1 \iff 3y = 7 \implies \bf y = \dfrac{7}{3}\\[/tex]
⇒
[tex]\dfrac{3x - y}{x+y} \cdot \dfrac{1}{7} = \dfrac{3(3) - \frac{7}{3} }{7(3+\frac{7}{3} )} = \dfrac{9 - \frac{7}{3} }{7(\frac{16}{3})} = \dfrac{\frac{27-7}{3} }{7(\frac{16}{3})}=\\[/tex]
[tex]= \dfrac{\frac{20}{3} }{\frac{112}{3}} = \dfrac{20}{3} : \dfrac{112}{3} = \dfrac{20}{3} \cdot \dfrac{3}{112} = \dfrac{20}{112} = \bf \dfrac{5}{28}\\[/tex]
Faster please!! thank u!! If the length of side DF = 4 ft., what is the length of side GH?
The length of GH on the triangle is 12 units
How to determine the length of GHFrom the question, we have the following parameters that can be used in our computation:
The similar triangles
Assuming that
The smaller triangle with length DF gives the larger triangle with length GH
This means that
GH = 3 * DF
Substitute the known values in the above equation, so, we have the following representation
GH = 3 * 4
So, we have
GH = 12
Hence, the length is 12 units
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Answer:
12 ft
Step-by-step explanation:
keep it simple, just givin' the answer :)
0
T
1
0 10
لسل
5
8
Centimeters
3
2
2
Millimeters
4 5
20 30 40 50
There is a proportional relationship between any length
measured in centimeters (cm) and the same length
measured in millimeters (mm).
Use the ruler to help you complete the table.
Length (mm)
884
25
240
699.1
Length (cm)
What is the constant of proportionality?
ONDE
Submit
Sign out
US
The proportionality constant (mm to cm) is 10 and the complete table is -
9 cm 90 mm
12.5 cm 125 mm
50 cm 500 mm
88.49 cm 884.9 mm
What is proportional relationship?A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.
Given is a proportional relationship between two scales.
{ 1 } -
We can write the proportionality constant (mm to cm) as -
{k} = (20 - 10)/(2 - 1)
{k} = 10
{ 2 } -
We can write the complete table as -
9 cm 9 x 10 = 90 mm
12.5 cm 12.5 x 10 = 125 mm
50 cm 50 x 10 = 500 mm
88.49 cm 88.49 x 10 = 884.9 mm
Therefore, the proportionality constant (mm to cm) is 10 and the complete table is -
9 cm 90 mm
12.5 cm 125 mm
50 cm 500 mm
88.49 cm 884.9 mm
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PLEASE HELP PLEASE ASAP PLEASE HELP
What are the coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin?
The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are R' (2, 1), S' (4, 2), T' = (5, 4), and U' = (3, 3).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of triangle RSTU, the coordinates of the vertices of the image are as follows:
(x, y) → (-y, x)
Ordered pair R = (1, -2) → Ordered pair R' = (-(-2), 1) = (2, 1).
Ordered pair S = (2, -4) → Ordered pair S' = (-(-4), 2) = (4, 2).
Ordered pair T = (4, -5) → Ordered pair T' = (-(-5), 4) = (5, 4).
Ordered pair U = (3, -3) → Ordered pair U' = (-(-3), 3) = (3, 3).
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the number of square units for the area because Area=LW so A=10x10 which is 100 and perimeter is P=2L=2W so that would be P=2(10)+2(10) which is 40, therefore, the area is greater
The number of square units for the area of the square is greater than the number of units for the perimeter.
How can the area and perimeter of a square be calculated?The area of a square is calculated using the formula below:
Area of square = (length of side)²
The length of the side of the square = 10 units
Ares of the square = 10 * 10
Area of the square = 100 units
The perimeter of a square = 4 * length of the side
Perimeter of a square = 4 * 10
The perimeter of a square = 40
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Complete question:
One side of a square is 10 units. Which is greater the number of square units for the area of the square or the number of units for the perimeter?
Find the inverse of the function f(x)=√x+3.
Answer:
The inverse of the function is
[tex]f^{-1} (x)=x^2-3[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\sqrt{x+3}[/tex]
Find the inverse.
Write the function as an equation equal to [tex]y[/tex].
[tex]y=\sqrt{x+3}[/tex]
Interchange the variables.
[tex]x=\sqrt{y+3}[/tex]
Square both sides of the equation.
[tex]x^2=y+3[/tex]
Subtract [tex]3[/tex] from both sides of the equation.
[tex]y=x^2-3[/tex]
Replace [tex]y[/tex] with [tex]f^{-1} (x)[/tex].
[tex]f^{-1} (x)=x^2-3[/tex]
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1.1. Thembile is a second hand dealer. She bought the sewing machine for R5700 and later sold it for R8850. 1.1.1. How much profit/loss was made? Profit selling price - cost price
The profit made from Thembile selling the second hand sewing machine if the cost price is R5700 and the selling price is R8850 is R3150.
How much profit/loss was made?Profit/loss refers to the difference between the cost price and selling price of an item. When the difference is positive; it is profit. When the difference is negative; it is loss.
Cost profit = R5700
Selling price = R8850
Profit = Selling price - Cost price
= R8850 - R5700
= R3150
Ultimately, Thembile made a profit of R3150 on the second hand sewing machine.
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9. A number multiplied -32 is 256. What is the number?
Answer:
See below.
Step-by-step explanation:
We are asked for a unknown number.
To find our number, we should use the Inverse Operation.
What is the Inverse Operation?The Inverse Operation is the opposite operation.
For example: If we Multiplied, then we should use the Inverse Operation which is Dividing.
Let's divide 256 by -32 to identify our missing number.
Divide:
[tex]\frac{256}{-32} = -8[/tex]
Our missing number is -8.
15
The circle graph shows the percentages of a family budget used for different monthly expenses.
Family Budget
Utilities
20%
Gasoline
10%
Clothes
15%
Mortgage
30%
Groceries
25%
Which statement is supported by the data in the graph? 7.6G
A The amount of money budgeted for gasoline and clothes combined is greater than the amount budgeted for groceries.
B The amount of money budgeted for utilities and gasoline combined is less than the amount budgeted for the mortgage.
The amount of money budgeted for the mortgage is half of the amount budgeted for clothes.
The amount of money budgeted for groceries and clothes combined is twice the amount budgeted for utilities.
1. Given that
lim
x → a f(x) = 2, lim
x → a g(x) = −4, lim
x → a h(x) = 0
find the limits.
(a) lim
x → a [ f(x) + 2g(x)]
(b) lim
x → a [h(x) − 3g(x) + 1]
(c) lim
x → a [ f(x)g(x)] (d) lim
x → a [g(x)]2
(e) lim
x → a
3
√6 + f(x) (f ) lim
x → a
2
g(x)
The answers to all limits are:
(a) lim x → a [ f(x) + 2g(x)] = -6,
(b) lim x → a [h(x) − 3g(x) + 1] = 13
(c) lim x → a [ f(x)g(x)] = -8
(d) lim x → a [g (x)]² = 16
(e) lim x → a 3√6 + f(x) / 2g(x)
What is the algebraic limit theorem?The central limit theorem states that if you take sufficiently large samples from a population, the samples' means will be normally distributed, even if the population isn't normally distributed.
(a) lim x → a [ f(x) + 2g(x)]
= lim x → a f(x) + 2 lim x → a g(x) (using algebraic limit theorem)
= 2 + 2(-4)
= -6
(b) lim x → a [h(x) − 3g(x) + 1]
= lim x → a h(x) - 3 lim x → a g(x) + lim x → a 1 (using algebraic limit theorem)
= 0 - 3(-4) + 1
= 13
(c) lim x → a [ f(x)g(x)]
= lim x → a f(x) * lim x → a g(x) (using algebraic limit theorem)
= 2 * (-4)
= -8
(d) lim x → a [g(x)]²
= [lim x → a g(x)]^2 (using algebraic limit theorem)
= (-4)^2
= 16
(e) lim x → a 3√6 + f(x) / 2g(x)
= [3√6 + lim x → a f(x)] / [2 lim x → a g(x)] (using algebraic limit theorem)
= [3√6 + 2] / [2(-4)]
= (-3√6 - 2) / 8
Therefore, the answers to all limits are:
(a) lim x → a [ f(x) + 2g(x)] = -6,
(b) lim x → a [h(x) − 3g(x) + 1] = 13
(c) lim x → a [ f(x)g(x)] = -8
(d) lim x → a [g (x)]² = 16
(e) lim x → a 3√6 + f(x) / 2g(x)
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Dan has 16 pencils. Quentin gives him
5 more pencils. Choose all the ways you
can use to find how many pencils Dan
has in all.
016 +5
o 16 + 4+
o 16-5
16 + 5
Because Dan has 16 pencils and he gets 5 more
If the given sample variance is 17.56, what is the standard deviation?
According to the preceding statement, then standard deviation becomes 4.19 if the sample variance is given as 17.56.
How to interpret a standard deviation?A measurement of a data set's departure from the mean is referred to as "standard deviation" (or ""). Whereas a large variance shows that the numbers are more spread, a lower number suggests that its data are clustered around the mean. The standard deviation is a measure of how volatile your collected data is generally. It displays the standard deviation for every score with respect to the mean.
We must consider the square root of both the sample covariance matrix to determine the standard deviation.
= √17.56
≈ 4.19
Hence, their standard deviation is around 4.19
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the graph y=x^2 and x=y^2, show the similarities and differences
One key difference between the two graphs is that [tex]$y=x^2$[/tex] is a function, meaning that for each x value there is only one y value. On the other hand,[tex]$x=y^2$[/tex]is not a function.
How to find similarities and differences between graphs?The graph of[tex]$y=x^2$[/tex] is a parabola that opens upwards, centered at the origin (0,0). The graph of [tex]$x=y^2$[/tex] is also a parabola, but it opens to the right, also centered at (0,0). Both graphs intersect at the origin, where x=y=0.
Another important similarity between the two graphs is that they are both symmetric with respect to the y=x line,
which is the line of symmetry for both graphs. This means that if we reflect one of the graphs across the line y=x, we get the other graph.
One key difference between the two graphs is that [tex]$y=x^2$[/tex] is a function, meaning that for each x value there is only one y value.
On the other hand,[tex]$x=y^2$[/tex]is not a function, because for some y values there are two corresponding x values (one positive and one negative). This means that the graph of [tex]$x=y^2$[/tex] fails the vertical line test.
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The equation Q=2s2+4sh represents the surface area, Q, of a cracker box in the shape of a square prism with a base side length of
In square prism , A cracker box in the shape of a square prism with a base side length of [tex]SA - \frac{2S^{2} }{4S} = h[/tex].
What is square prism?
The bases of a square prism are square, and the other four faces are rectangles. A square prism is a cuboid object in three dimensions.
Angles and sides that are in opposition to one another are congruent. A magnet bar is an illustration of the shape of a square prism.
we know that'
The formula to calculate the surface area of a square prism is
[tex]Q = 2s^{2} + 4sh[/tex]
subtract 2s² both sides
SA - 2s² = 4sh
Divide by 4s both sides
[tex]SA - \frac{2S^{2} }{4S} = h[/tex]
Rewrite
[tex]SA - \frac{2S^{2} }{4S} = h[/tex]
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The perimeter of a rectangular fence is to be at least 82 feet and no more than 124 feet. If the width of the fence is 14 feet, what is the range of values for the length of the fence?
The range of values for length when the perimeter is between 82 feet and 124 feet is: 27 ≤ l ≤ 48
What is meant by perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter. The perimeter of the shape can be calculated by summing the measurements of its sides and edges. A rectangle's perimeter is equal to twice the product of its length and width.
Given a rectangular fence.
The perimeter P is at least 82 feet and is no more than 124 feet.
82 ≤ P ≤ 124
The width is 14 feet.
The range of values of the length is to be found.
Now,
Perimeter of rectangle = 2( length + width)
The lowest value of the perimeter is 82
82 = 2(l + 14)
82 = 2l + 28
54 = 2l
l = 27
The highest value of perimeter is 124
124 = 2(l + 14)
124 = 2l +28
96 = 2l
l = 48
Therefore the range of values for length when the perimeter is between 82 feet and 124 feet is:
27 ≤ l ≤ 48
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